Помогите, пожалуйста, вычислить интеграл
int (0 2^(1/2)) ((2 + x^2)^(1/2) - (2 - x^2)^(1/2))/(4 - x^4)^(1/2) dx
int (0 2^(1/2)) ((2 + x^2)^(1/2) - (2 - x^2)^(1/2))/(4 - x^4)^(1/2) dx =
= int (0 2^(1/2)) ((2 + x^2)^(1/2) - (2 - x^2)^(1/2))/((2 - x^2) * (2 + x^2))^(1/2) dx =
= int (0 2^(1/2)) ((2 + x^2)^(1/2) -
- (2 - x^2)^(1/2))/((2 - x^2)^(1/2) * (2 + x^2)^(1/2)) dx =
= int (0 2^(1/2)) 1/(2 - x^2)^(1/2) dx - int (0 2^(1/2)) 1/(2 + x^2)^(1/2) dx =
= (arcsin x/2^(1/2))_{0}^{2^(1/2)} - (ln |x + (2 + x^2)^(1/2)|)_{0}^{2^(1/2)} =
= (arcsin 1 - arcsin 0) - (ln (2^(1/2) + 2) - ln 2^(1/2)) =
= pi/2 - ln ((2^(1/2) + 2)/2^(1/2)) = pi/2 - ln (1 + 2^(1/2))
Спасибо большое!!!
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